According to cops, Farrah and Debra started arguing over childcare issues when Debra allegedly threw an MTV shirt at her daughter ... which landed "on or near" Farrah's baby, who started crying.

That's when Farrah claims she went off on her mother -- who then grabbed Farrah by the throat. Farrah told cops she pushed her mother's hand away from her throat, causing her mother to strike her on the right side of her head and mouth.

In the report, officers say they observed multiple cuts on the right side of Farrah's lips.